if you want to dig a little. Find the two wires coming from the switch. Trace them to the motherboard connectors. The switch is the "momentary" type which means the contacts close the connection on the wires only while the button is pressed. You can do the same thing with a small screwdriver between the two connectors on the motherboard. If it powers up every time, the switch is bad, a not uncommon occurrence.
You might find a replacement switch here, input the PC make and model number.
My mom has a Dell Dimension 5100 and the on/off switch to the CPU seems to be bad. Sometimes it turns the computer on, sometimes it doesn't. She thinks she needs a new on/off switch.
I've scoured the net and can't find one anywhere. Some folks sell old ones pulled from working computers on eBay, but none match the 5100.
1. Is it really likely that it's the switch that's bad? The computer does occasionally power up.
2. Where the heck can I find a switch???